Spm physics-formula-list-form4

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Physics Equation List :Form 4
Introduction to Physics
Relative Deviation

Relative Deviation = Mean Deviation ×100%
Mean Value
Prefixes

Prefixes Value Standard form Symbol
Tera 1 000 000 000 000 1012 T
Giga 1 000 000 000 109 G
Mega 1 000 000 106 M
Kilo 1 000 103 k
deci 0.1 10-1 d
centi 0.01 10-2 c
milli 0.001 10-3 m
micro 0.000 001 10-6 μ
nano 0.000 000 001 10-9 n
pico 0.000 000 000 001 10-12 p

Units for Area and Volume

1 m = 102 cm (100 cm) 1
2 4 2 2 1 cm = 10-2 m ( m)
1 m = 10 cm (10,000 cm ) 100
1 m3 = 106 cm3 (1,000,000 cm3) 1
1 cm2 = 10-4 m2 ( m2 )
10,000
1
1 cm3 = 10-6 m3 ( m3 )
1,000,000

http://www.one-school.net/notes.html 1

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Force and Motion
Average Speed

Average Speed = Total Distance
Total Time
Velocity

(ms-1)
v= s
v = velocity
s = displacement (m)
t t = time (s)

Acceleration

v−u a = acceleration (ms-2)
a= v = final velocity
u = initial velocity
(ms-1)
(ms-1)
t t =time for the velocity change (s)

Equation of Linear Motion

Linear Motion

Motion with Motion with
Motion with
constant changing
constant velocity
acceleration acceleration

s v = u + at Using Calculus
v= (In Additional
t 1
s = (u + v)t Mathematics
2 Syllabus)
1
s = ut + at 2
2
v 2 = u 2 + 2as

u = initial velocity (ms-1)
v = final velocity (ms-1)
a = acceleration (ms-2)
t = time (s)


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Ticker Tape

Finding Velocity:

s
velocity =
number of ticks × 0.02s

1 tick = 0.02s

Finding Acceleration:

v−u
a=
t
a = acceleration (ms-2)
v = final velocity (ms-1)
t = time for the velocity change (s)

Graph of Motion

Gradient of a Graph The gradient 'm' of a line segment between two
points and is defined as follows:

Change in y coordinate, Δy
Gradient, m =
Change in x coordinate, Δx
or
Δy
m=
Δx


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Displacement-Time Graph Velocity-Time Graph

Gradient = Velocity (ms-1) Gradient = Acceleration (ms-2)
Area in between the graph and x-axis =
Displacement

Momentum

p = m×v p = momentum
m = mass
(kg ms-1)
(kg)
v = velocity (ms-1)

Principle of Conservation of Momentum

m1u1 + m2u2 = m1v1 + m2 v2
m1 = mass of object 1 (kg)
m2 = mass of object 2 (kg)
u1 = initial velocity of object 1 (ms-1)
u2 = initial velocity of object 2 (ms-1)
v1 = final velocity of object 1 (ms-1)
v2 = final velocity of object 2 (ms-1)

Newton’s Law of Motion
Newton’s First Law

In the absence of external forces, an object at rest remains at rest and an object in motion continues in
motion with a constant velocity (that is, with a constant speed in a straight line).


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Newton’s Second Law

mv − mu The rate of change of momentum of a body is directly proportional to the
Fα resultant force acting on the body and is in the same direction.
t F = Net Force (N or kgms-2)
m = mass (kg)
F = ma a = acceleration (ms-2)

Implication
When there is resultant force acting on an object, the object will accelerate
(moving faster, moving slower or change direction).

Newton’s Third Law

Newton's third law of motion states that for every force, there is a reaction force with the same magnitude
but in the opposite direction.

Impulse

Impulse = Ft F = force
t = time
(N)
(s)

Impulse = mv − mu m = mass
v = final velocity
(kg)
(ms-1)

Impulsive Force

mv − mu F = Force (N or kgms-2)
F= t = time
m = mass
(s)
(kg)
t v = final velocity (ms-1)

Gravitational Field Strength

g = gravitational field strength (N kg-1)
F
g= F = gravitational force
m = mass
(N or kgms-2)
(kg)
m
Weight

W = mg W = Weight
m = mass (kg)
(N or kgms-2)

g = gravitational field strength/gravitational acceleration (ms-2)


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Vertical Motion

• If an object is release from a high position: • If an object is launched vertically upward:
• The initial velocity, u = 0. • The velocity at the maximum height, v = 0.
• The acceleration of the object = gravitational • The deceleration of the object = -gravitational
acceleration = 10ms-2(or 9.81 ms-2). acceleration = -10ms-2(or -9.81 ms-2).
• The displacement of the object when it reach the • The displacement of the object when it reach the
ground = the height of the original position, h. ground = the height of the original position, h.

Lift
In Stationary
• When a man standing inside an elevator, there
are two forces acting on him.
(a) His weight， which acting downward.
(b) Normal reaction (R), acting in the opposite
direction of weight.

• The reading of the balance is equal to the normal
reaction.

R = mg


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Moving Upward with positive acceleration Moving downward with positive acceleration

R = mg + ma R = mg − ma
Moving Upward with constant velocity Moving downward with constant velocity.

R = mg R = mg
Moving Upward with negative acceleration Moving downward with negative acceleration

R = mg − ma R = mg + ma


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Smooth Pulley

With 1 Load
Moving with uniform speed:

T1 = T2 T1 = mg

Stationary: Accelerating:

T1 = mg T1 – mg = ma

With 2 Loads
Finding Acceleration:
(If m2 > m1)
m2g – m1g = (m1+ m2)a

Finding Tension:
(If m2 > m1)
T1 = T2
T1 – m1g = ma
m2g – T2 = ma

Vector

Vector Addition (Perpendicular Vector)
Magnitude = x2 + y2

| y|
Direction = tan −1
| x|

Vector Resolution

| x |=| p | sin θ
| y |=| p | cosθ


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Inclined Plane

Component parallel to the plane = mgsinθ

Component perpendicular to the plane = mgcosθ

Forces In Equilibrium

T3 = mg T3 = mg

T2 sin θ = mg T2 cosθ = T1 cos α

T2 cosθ = T1 T2 sin θ + T1 sin α = mg

T1 tan θ = mg

Work Done

W = Fx cos θ W = Work Done (J or Nm)
F = Force (N or kgms-2)
x = displacement (m)
θ = angle between the force and the direction of motion (o )

When the force and motion are in the same direction.

W = Fs W = Work Done
F = Force
(J or Nm)
(N or kgms-2)


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Energy

Kinetic Energy
1 EK = Kinetic Energy (J)
EK = mv 2 m = mass (kg)
2 v = velocity (ms-1)

Gravitational Potential Energy
EP = mgh EP = Potential Energy
m = mass
(J)
(kg)
g = gravitational acceleration (ms-2)
h = height (m)

Elastic Potential Energy
1 EP = Potential Energy (J)
EP = kx 2 k = spring constant (N m-1)
2 x = extension of spring (m)
1
EP = Fx F = Force (N)
2
Power and Efficiency

Power
W P = power (W or Js-1)
P= W = work done (J or Nm)
t E = energy change (J or Nm)
E t = time (s)
P=
t
Efficiency
Useful Energy
Efficiency = × 100%
Energy
Or

Power Output
Efficiency = × 100%
Power Input
Hooke’s Law

F = kx F = Force
k = spring constant
(N or kgms-2)
(N m-1)
x = extension or compression of spring (m)


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Force and Pressure
Density

m
ρ=
V
ρ = density (kg m-3)
m = mass (kg)
V = volume (m3)
Pressure

F P = Pressure (Pa or N m-2)
P= A = Area of the surface (m2)
A F = Force acting normally to the surface (N or kgms-2)

Liquid Pressure
P = hρ g h = depth (m)
g = gravitational Field Strength (N kg-1)

Pressure in Liquid
P = Patm + h ρ g h = depth (m)
g = gravitational Field Strength (N kg-1)
Patm = atmospheric Pressure (Pa or N m-2)

Gas Pressure

Manometer

P = Patm + h ρ g
Pgas = Pressure (Pa or N m-2)

Patm = Atmospheric Pressure (Pa or N m-2)



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U=tube
h1 ρ1 = h2 ρ 2

Pressure in a Capillary Tube

Pgas = gas pressure in the capillary tube (Pa or N m-2)
Patm = atmospheric pressure (Pa or N m-2)
h = length of the captured mercury (m)
ρ = density of mercury (kg m-3)
Barometer

Pressure in unit cmHg Pressure in unit Pa

Pa = 0 Pa = 0
P b = 26 P b = 0.26×13600×10
P c = 76 P c = 0.76×13600×10
P d = 76 P d = 0.76×13600×10
P e = 76 P e = 0.76×13600×10
P f = 84 P f = 0.84×13600×10

(Density of mercury = 13600kgm-3)


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Pascal’s Principle

F1 F2
=
A1 A2
F1 = Force exerted on the small piston
A1 = area of the small piston
F2 = Force exerted on the big piston
A2 = area of the big piston

Archimedes Principle

Weight of the object, W = ρ1V1 g

Upthrust, F = ρ 2V2 g

ρ1 = density of wooden block
V1 = volume of the wooden block
ρ2 = density of water
V2 = volume of the displaced water
g = gravitational field strength

Density of water > Density of wood Density of Iron > Density of water

F=T+W T+F=W
ρVg = T + mg ρVg + T = mg


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Heat

Heat Change
Q = mcθ
m = mass (kg)
c = specific heat capacity (J kg-1 oC-1)
θ = temperature change (o)

Electric Heater Mixing 2 Liquid

Energy Supply, E = Pt Heat Gain by Liquid 1 = Heat Loss by Liquid 2
Energy Receive, Q = mcθ m1c1θ1 = m2 c2θ 2
Energy Supply, E = Energy Receive, Q m1 = mass of liquid 1
c1 = specific heat capacity of liquid 1
Pt = mcθ θ1 = temperature change of liquid 1

E = electrical Energy (J or Nm) m2 = mass of liquid 2
P = Power of the electric heater (W) c2 = specific heat capacity of liquid 2
t = time (in second) (s) θ2 = temperature change of liquid 2

Q = Heat Change (J or Nm)
m = mass (kg)
c = specific heat capacity (J kg-1 oC-1)
θ = temperature change (o)

Specific Latent Heat

Q = mL
Q = Heat Change (J or Nm)
m = mass (kg)
L = specific latent heat (J kg-1)

Boyle’s Law

PV1 = P2V2
1

(Requirement: Temperature in constant)
Pressure Law

P P2
1
=
T1 T2
(Requirement: Volume is constant)


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Charles’s Law

V1 V2
=
T1 T2
(Requirement: Pressure is constant)
Universal Gas Law
PV1 PV2
1
= 2
T1 T2
P = Pressure (Pa or cmHg …….)
V = Volume (m3 or cm3)
T = Temperature (MUST be in K(Kelvin))

Light
Refractive Index

Snell’s Law
Real depth/Apparent Depth
sin i
n=
sin r
n = refractive index (No unit)
i = angle of incident (o)
r = angle of reflection (o )

D
n=
d
n = refractive index (No unit)
D = real depth (m or cm…)
d = apparent depth (m or cm…)

Speed of light Total Internal Reflection
c 1
n= n=
v sin c
n = refractive index (No unit) n = refractive index (No unit)
c = speed of light in vacuum (ms-1) c = critical angle (o )
v = speed of light in a medium (like water,
glass …) (ms-1)


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Lens

Power
1
P=
f
P = Power (D(Diopter))
f = focal length (m)

Linear Magnification
hi v hi v
m= m= =
ho u ho u

m = linear magnification (No unit)
u = distance of object (m or cm…)
v = distance of image (m or cm…)
hi = heigth of image (m or cm…)
ho = heigth of object (m or cm…)

Lens Equation

Conventional symbol
positive negative
1 1 1 u Real object Virtual object
+ =
u v f v Real image Virtual image

f Convex lens Concave lens


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Astronomical Telescope

Magnification,
Pe fo
m= m=
Po fe
m = linear magnification
Pe = Power of the eyepiece
Po = Power of the objective lens
fe = focal length of the eyepiece
fo = focal length of the objective lens

Distance between eye lens and objective lens

d = fo + fe

d = Distance between eye lens and objective lens

Compound Microscope

Magnification
m = m1 × m2
Height of first image , I1 Height of second image, I 2
= ×
Height of object Height of first image , I1
Height of second image, I 2
=
Height of object, I1

m = Magnification of the microscope
m1 = Linear magnification of the object lens
m2 = Linear magnification of the eyepiece

Distance in between the two lens
d > fo + fe

d = Distance between eye lens and objective lens


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